Abstract

Supermassive black holes with up to a 10$^{9}$ M$_{⊙}$ dwell in the centres of present-day galaxies, and their presence has been confirmed at z {\ge} 6. Their formation at such early epochs is still an enigma. Different pathways have been suggested to assemble supermassive black holes in the first billion years after the big bang. Direct collapse has emerged as a highly plausible scenario to form black holes as it provides seed masses of 10$^{5}$-10$^{6}$ M$_{⊙}$. Gravitational collapse in atomic cooling haloes with virial temperatures T$_{vir}$ {\ge} 10$^{4}$ K may lead to the formation of massive seed black holes in the presence of an intense background ultraviolet flux. Turbulence plays a central role in regulating accretion and transporting angular momentum. We present here the highest resolution cosmological large eddy simulations to date which track the evolution of high-density regions on scales of 0.25 au beyond the formation of the first peak, and study the impact of subgrid-scale turbulence. The peak density reached in these simulations is 1.2 {\times} 10$^{-8}$ g cm$^{-3}$. Our findings show that while fragmentation occasionally occurs, it does not prevent the growth of a central massive object resulting from turbulent accretion and occasional mergers. The central object reaches {\tilde}1000 M$_{⊙}$ within four free-fall times, and we expect further growth up to 10$^{6}$ M$_{⊙}$ through accretion in about 1 Myr. The direct collapse model thus provides a viable pathway of forming high-mass black holes at early cosmic times.